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Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains

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Abstract

The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial velocity in some precise sense. Using the energy method with the estimates of boundary integrals, we obtain the a priori bounds of the density and velocity field. Finally, we establish the blowup criterion for the 3D combustion system.

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Acknowledgements

The author would particularly like to acknowledge Professor Jing Li, for providing this problem and inspiring its interest in partial differential equations. The author would also like to thank the referee for his/her valuable comments and careful reading of the manuscript.

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  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Jiawen Zhang

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Zhang, J. Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains. J. Math. Fluid Mech. 25, 86 (2023). https://doi.org/10.1007/s00021-023-00830-7

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